Knowledge:
The student will obtain detailed understanding of K-theory and
learn basic facts about K-homology, cyclic cohomology and
characteristic classes. The student will have a basic understanding
of the applications of homological methods for both topological
spaces and non-commutative C*-algebras

Skills:
At the end of the course the student will be able to prove basic
properties of topological K-theory and K-homology, demonstrate the
ability to compute it in some examples. He/she will have a basic
knowledge of yclic theory

Competences:
The student will be able to use K-theory, K-homology and cyclic
homology in both topological and C*-algebraic
problems.